I suspect we're encountering a planning vs logging fork here. If you primarily use a daily page to log or track what you did, then terms like journal or diary s

I suspect we're encountering a planning vs logging fork here. If you primarily use a daily page to log or track what you did, then terms like journal or diary seem most natural to you. If you primarily use it to plan or list what you need to do in the future, then you're more likely to call it a day planner. HN seems more highly populated with loggers and trackers compared to the general public. A quick search on Amazon US for "day planner", "journal", and "diary" suggests most people associate journal and diary with free-form pages and day planner with date-based pages (implying most people who use date-based pages are more planners than loggers)